/MAT/LAW121 (PLAS_RATE)
Block Format Keyword Elastoplastic strainrate dependent material with isotropic von Mises yield criterion. This material law is available for both solids and shells.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW121/mat_ID/unit_ID or /MAT/PLAS_RATE/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\nu $  Ires  Ivisc  F_{cut}  DTMIN  
Fct_SIG0  Xscale_SIG0  Yscale_SIG0  
Fct_YOUN  Xscale_YOUN  Yscale_YOUN  
Fct_TANG  Xscale_TANG  TANG  
Fct_FAIL  Ifail  Xscale_FAIL  Yscale_FAIL 
Definition
Field  Contents  SI Unit Example 

mat_ID  Material identifier. (Integer, maximum 10 digits) 

unit_ID  (Optional) Unit
identifier. (Integer, maximum 10 digits) 

mat_title  Material title. (Character, maximum 100 characters) 

${\rho}_{i}$  Initial
density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young’s
modulus. (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  Poisson’s
ratio. (Real) 

Ires  Resolution method for plasticity.
(Integer) 

Ivisc  Strain rate dependency formulation.
(Integer) 

Ifail  Failure criterion variable (used
only Fct_FAIL > 0).
(Integer) 

F_{cut}  Cutoff frequency for strain rate
filtering (used only Ivisc =
0). Default = 10000 Hz (Real) 
$\text{[Hz]}$ 
DTMIN  Minimum time step size for
automatic element deletion. Default = 0.0 (Real) 
$\left[\text{s}\right]$ 
Fct_SIG0  Yield stress versus effective
strain rate function identifier. (Integer) 

Xscale_SIG0  Scale factor for abscissa (strain
rate) in Fct_SIG0. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Yscale_SIG0  Scale factor for ordinate (stress)
in Fct_SIG0. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fct_YOUN  Young’s modulus versus effective
strain rate function identifier (available only
Ivisc = 0). Default = 1.0 (Real) 

Xscale_YOUN  Scale factor for abscissa (strain
rate) in Fct_YOUN. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Yscale_YOUN  Scale factor for ordinate (stress)
in Fct_YOUN. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fct_TANG  Plastic tangent modulus versus
effective strain rate function
identifier. (Integer) 

Xscale_TANG  Scale factor for abscissa (strain
rate) in Fct_TANG. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
TANG 

$\left[\text{Pa}\right]$ 
Fct_FAIL  Failure criterion variable versus
effective strain rate function
identifier. (Integer) 

Xscale_FAIL  Scale factor for abscissa (strain
rate) in Fct_FAIL. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Yscale_FAIL  Scale factor for ordinate (stress)
in Fct_FAIL. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Example (Steel)
#12345678910
/UNIT/1
Unit system
Mg mm s
#12345678910
/MAT/LAW121/1/1
Steel
# RHO_I
7.85E9
# E Nu Ires Ivisc Fcut DTMIN
194200.0 0.3 1 0 1000 0
# Fct_SIG0 Xscale_SIG0 Yscale_SIG0
5 0 0
# Fct_YOUN Xscale_YOUN Yscale_YOUN
6 0 0
# Fct_TANG Xscale_TANG TANG
7 0 0
# Fct_FAIL Ifail Xscale_FAIL Yscale_FAIL
8 1 0 0
#12345678910
/FUNCT/5
Yield stress versus effective strain rate
0.0 272.2
1000.0 572.2
#12345678910
/FUNCT/6
Young’s modulus versus effective strain rate
0.0 192400.0
1000.0 272400.0
#12345678910
/FUNCT/7
Plastic tangent modulus versus effective strain rate
0.0 4500.0
1000.0 6500.0
#12345678910
/FUNCT/8
Failure criterion variable versus effective strain
0.0 0.15
1000.0 0.25
#12345678910
#ENDDATA
/END
#12345678910
Comments
 This material law considers isotropic and linear elasticity.
 The plastic behavior is described with a classical von Mises
plasticity yield function described with:
(1) $$f={\sigma}_{VM}{\sigma}_{Y}$$With:(2) $${\sigma}_{VM}=\sqrt{\frac{3}{2}s:s}$$Where, $s$ is the deviatoric stress tensor.
 The yield stress is strain rate dependent and described
as:
(3) $${\sigma}_{Y}={\sigma}_{0}(\dot{\epsilon})+\frac{E(\dot{\epsilon}){E}_{t}(\dot{\epsilon})}{E(\dot{\epsilon}){E}_{t}(\dot{\epsilon})}{\epsilon}_{p}$$Where, ${\sigma}_{0}$
 Strain rate dependent initial yield stress defined by function Fct_SIG0.
 $E(\dot{\epsilon})$
 Young’s modulus that may optionally depend on the strain rate (if Fct_YOUN is defined).
 ${E}_{t}(\dot{\epsilon})$
 Plastic tangent modulus that may optionally depend on the strain rate (if Fct_TANG is defined).
 ${\epsilon}_{p}$
 Cumulative plastic strain.
Note: The inequality $E(\dot{\epsilon})>{E}_{t}(\dot{\epsilon})$ must always be fulfilled. If not, the solver will automatically limit the value of the tangent modulus ${E}_{t}(\dot{\epsilon})=0.99\times E(\dot{\epsilon})$ .  Two strain rate dependency formulations are available depending on
the value of the flag Ivisc.
 Ivisc = 0: scaled yield stress
formulation. In this case, the strain rate corresponds to the total
effective strainrate computed as:
(4) $$\dot{\epsilon}=\sqrt{\frac{2}{3}\dot{\epsilon}\text{'}:\dot{\epsilon}\text{'}}$$Where, $\dot{\epsilon}\text{'}$ is the deviatoric total strain rate tensor.
For this formulation, all strain rate dependent variables are updated at the beginning of the timestep and are constant during the return mapping algorithm. All strain rate dependent variables are allowed using this formulation. The strain rate is, in this case, filtered by default as:(5) $${\dot{\epsilon}}_{{}_{f}}^{n}=\alpha {\dot{\epsilon}}^{n}+(1\alpha ){\dot{\epsilon}}_{f}^{n1}$$Where, $\alpha =2\pi {F}_{cut}\text{\Delta}t$ .
You can then adapt the filtering by specifying a value for the cutoff frequency F_{cut}. This formulation is lighter and faster than the viscoplastic one described below.
 Ivisc = 1: viscoplastic
formulation. In this case, the strain rate corresponds to the
plastic strain rate.
(6) $$\dot{\epsilon}={\dot{\epsilon}}_{p}$$In this case, the strain rate is initially null, and is computed and updated during the return mapping procedure. All strain rate dependent variable variations are taken into account leading to a heavier cost of computation. However, no strain rate filtering is needed, and you can speed up the simulation using the NICE explicit return mapping (Ires = 1). This formulation, the Young’s modulus is not allowed to vary with strain rate.
 Ivisc = 0: scaled yield stress
formulation. In this case, the strain rate corresponds to the total
effective strainrate computed as:
 You can choose the algorithm of return mapping to find a compromise
between precision and cost. Two return mapping methods are available.
 Ires = 1: the NICE explicit method (Next Increment Correct Error). This procedure only requires 1 iteration and uses a selfcorrecting ability to still preserve a good precision. This method can dramatically speed up the simulation.
 Ires = 2: the CuttingPlane (Newton iteration) method. This procedure requires several iterations (usually between 3 and 5) to solve the material behavior nonlinear equations. It is more expensive than the NICE explicit method but offers very good precision. This method is set by default.
 You can choose to add failure in the material behavior. To do so, a
function Fct_FAIL must be defined to describe the
evolution of the failure criterion variable with the strain rate. The nature
of the failure criterion variable is chosen using the flag
Ifail:
 Ifail = 0: the criterion is fulfilled when the von Mises stress reaches the critical value defined in the function
 Ifail = 1: the criterion is fulfilled when the cumulative plastic strain reaches the value defined in the function
 Ifail = 2: the criterion is fulfilled when the maximum principal stress or the absolute value of the minimum principal stress reaches the critical value defined in the function
 Ifail = 3: the criterion is fulfilled when the maximum principal stress reaches the critical value defined in the function
 Automatic element deletion can also be set if the element timestep decreases to reach a critical value defined by DTMIN.